Time Series over Tea
Time Series over Tea
Customized course notes for Time Series in Financial Mathematics
About the Book
This is a customized set of notes written collaboratively with AI. We are writing in real time to accompany the class in the University of Minnesota's Masters in Financial Mathematics program. New sections will be added on a weekly basis through May 2025.
About the Author
Table of Contents
- Introduction to STL (Seasonal-Trend Decomposition using LOESS)
- Fundamental Decomposition
- LOESS (Locally Estimated Scatterplot Smoothing)
- STL Algorithm
- Key Parameters
- Properties and Advantages
- Connection to Financial Time Series
- Seasonal Trend Decomposition using Loess, via o3-mini-high
- Historical Context and Development
- Mathematical Underpinnings
- Key Differences between parametric and non-parametric models
- Key Parameters: Seasonal Window and Trend Window
- How Loess Works Within STL
- Comparison with ARIMA Modeling
- Concluding Remarks
- Workflow for analysis
- Final Thoughts
- What are your time series goals?
- Time Series Cross-Validation: Best Practices
- Time Series vs. Traditional ML Cross-Validation
- Time Series Cross-Validation Methods
- Financial Time Series Considerations
- Comparison with Traditional ML Cross-Validation
- Implementation Best Practices
- Best Practices for Splitting Time Series Data
- Non-Time-Series Models
- Time Series Models
- Conclusion
- Cointegration a la ChatGPT
- 1. Integration and Unit Roots
- 2. Definition of Cointegration
- 3. The Error Correction Model (ECM)
- 4. The Johansen Method for Multivariate Cointegration
- 5. Estimation and Superconsistency
- Conclusion
- 1. Macroeconomic Relationships
- 2. ETFs and Pairs Trading
- 3. Agricultural Commodities
- 4. Metals Markets
- 5. Energy Markets
- Conclusion
- Pairs Trading from o3
- Mathematical Foundations of Cointegration
- Formal Definition and Properties
- Theoretical Framework: The Error Correction Model
- Testing for Cointegration
- Mathematical Properties of Cointegrated Systems
- Fractional Cointegration
- Applications of Cointegration in Economics and Quantitative Finance
- Macroeconomic Applications
- Equity Market Applications
- Commodity Market Applications
- Practical Implementation Considerations
- Seasonality and Cointegration Analysis
- Identifying and Testing Seasonal Effects in Cointegrated Series
- Approaches to Handling Seasonality in Cointegration
- Practical Examples in Financial Markets
- Advanced Modeling Considerations
- Statistical Tests for Seasonality in Cointegrated Systems
- Practical Implementation Recommendations
- Cointegration-Based Pairs Trading Strategy: Step-by-Step Implementation
- 1. Pair Selection Process
- 2. Model Calibration
- 3. Signal Generation
- 4. Position Sizing and Risk Management
- 5. Execution Strategy
- 6. Specific ETF Pair Examples
- 7. Ongoing Monitoring and Maintenance
- 8. Advanced Enhancements
- Introduction to STL (Seasonal-Trend Decomposition using LOESS)
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